Test the series below for convergence using the Root Test. n=1 f(n) 5n 9n + 3 The limit of the root test simplifies to lim f(n) where n→∞ = n The limit is: (enter oo for infinity if needed) Based on this, the series

Q: QUESTION 17 Determine the value of the second-order partial derivative f (1,0) of the following…

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Q: 2. Given: f(x) = x³ + 2x² (x - 1)²¹ with f'(x) x³ - 3x² 4x (x - 1)³ 14x + 4 (x - 1)4* 1 and y = x +…

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Q: Solve the system by back substitution. 4x+8y + 2z +6w= -4 -3y-18z-6w= -24 3z + 3w= 4w = 6 12 The…

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Q: 1. A homogeneous function is one such that f(tx, ty) = ta f(x, y) for some a. (a) Show that f(x, y)…

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A: D=x,y|3x2+3y2≤45

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Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) 1 X + 4…

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Q: Suppose that the monthly cost, in dollars, 70 chairs are produced monthly. a) What is the current…

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Q: Assume that C(x) is in dollars and x is the number of units produced and sold. For the total-cost…

A: △C=C(x+∆x)-C(x)△C=C(90+1)-C(90)△C=C(91)-C(90)   for x = 90 for x = 91 △C=C(91)-C(90)=167.41 -…

Q: Find the following for the vectors u = - 8i-10j + √3k and v=8i + 10j-√3k. a. v. u, |v|, and lu b.…

A: I am attaching image so that you understand each and every step.

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Q: The function f has a domain of [0, 4] and a range of [0, 2]. Start by sketching a potential graph of…

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Q: onsider the following. y=e-x² ind y'. ind the slope m of the tangent line to the graph of y = e-x²…

A: Given query is to find the equation of the tangent line.

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Q: Use the sum and difference identities to rewrite the following expression as a trigonometric…

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Q: How much work does it take to slide a crate 28 m along a loading dock by pulling on it with a 240-N…

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Q: The measurements of the base and altitude of a triangle are found to be 75 cm and 30 cm, with…

A: Let base of the triangle = baltitude = a hypotaneous = h Given b = 75 , a = 30 db = 0.15 , da = 0.10…

Q: QUESTION 12 A firm produces two types of toy trains each week. The weekly revenue function is given…

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Q: Consider the circle C of radius 4, centered at the origin. (a) Find a parametrization for C inducing…

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Q: 1. Apply Bisection method to find the root (only one root) of the function: f(x) = 8x^3 – 16x^2 + x…

A: Let's find root by using bisection method.

Q: 00 (-1)k For the convergent alternating series k=0 (3k+2) S-S in using the nth partial sum S to…

A: Concept: A series called an alternating series has terms that alternate between positive and…

Q: What

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Q: Find the equation of the tangent plane to the surface at the point (3,1,-1). x = y² + z² + 1

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Q: 3. A 13 ft ladder is sliding down a wall as depicted below. Use the Pythagorean Theorem x² + y² =…

A: we need to find out the rate at which the ladder is sliding down the wall.

Q: Applications of Differential Equations 7. A tank contains 200 liters of fluid in which 30 grams of…

A: Question number 7 can be solved using the concept of linear differential equation.Question number 8…

Q: y = x + X- 1 1- x X 1 X-1

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Q: An athlete puts a 16-lb shot at an angle of 60° to the horizontal from 6.5 ft above the ground at an…

A: Angle from the ground= 60° Initial speed = 42 feet/sec  Initial height = 6.5 feet

Q: (1) (1 + √√3i) Place all answers in the following blank, separated by commas: 2^(-2/3) (sqrt(3) + i)…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: y² + xy - 2x = x²

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

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Q: Read the micrometer. 10. 5- 44E -20 15 The length shown on the micrometer is (Type a whole number or…

A: To find the length on micrometer.

Q: Find the area inside r = 3 + 3 cos θ and outside r = 3 + 3 sin θ in the first quadrant

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Q: For f(x) = 5-x^2/3, show that f(-8) = f(8), but there is no number c in (-8,8) such that f'(c)=0.…

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Q: Rewrite the expression without the log of a product, power or root. 106₁ (2² √/²) = logg =

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Q: In this problem, p is in dollars and q is the number of units. Suppose that the demand for a product…

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Q: A 9 ft wide sheet of metal is used to make a water trough by bending up, at an angle 8, a 3 ft wide…

A: Given: A 9 ft wide sheet of metal is used to make a water trough by bending up, at an angle θ, a 3…

Q: Show your work Determine whether the series is convergent or divergent. Σκο-κ k=1

A: The given series is: ∑k=1∞ke-2k2 Determine whether the series is convergent or divergent.

Q: Solve. √4y+5-√√y-1 =3 Select the correct choice below and, if necessary, fill in the answer box to…

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Q: Determine whether the following series converge: a. Σ∞k=1 (1/√k3)

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Q: 3x + 5 Consider the function f(x) 52+1 (-∞, A) and (A, ∞o) where the function is not defined at A.…

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Q: 2. Evaluate 80-2[12-(5+4)]

A: we will find the required.

Q: If f(x) = 5√√x ln(x), find f'(x).

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Q: A particular computing company finds that its weekly profit, in dollars, from the production and…

A: NOTE: Refresh your page if you can't see any equations. . the profit function is  where x=number of…

Q: Express the vector - 6i- 2j-9k as a product of its length and direction. - 6i-2j-9k= 11 -[A-0-8] i+…

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Q: Find dy: 5x³ =-3xy + 2 dx ****

A: To find the derivative

Q: ind dy/dx and d²y/dx2 at the given point without eliminating the parameter. X= x= √√t, y=2t+4; t=1

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Q: Let f(x) ƒ'(0) = = 2e²+3 + e².

A: Given query is to find indicated derivative.